Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (CSE-IT)- Computer Science Engineering -Information Technology 2020 December 2nd Sem 76257 Mathematics Ii Previous Question Paper
Roll No.
Total No. of Pages : 03
Total No. of Questions : 18
B.Tech. (CSE/IT) (2018 & Onwards) (Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-204-18
M.Code : 76257
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION - B & C have FOUR questio ns eac h.
3 .
Attempt any FIVE questions from SECT ION B & C carrying EIGHT marks eac h.
4 .
Select atleast T WO que stions from SECT ION - B & C.
SECTION-A
Answer the following :
1.
Give any four characteristics for an ideal measure of dispersion.
2.
Define skewness.
3.
A bag contains 3 red, 6 white and 7 blue balls. What is the probability that two balls
drawn are white and blue?
4.
Give the formula of mean and standard deviation for Binomial distribution.
5.
Write any four properties of normal distribution.
6.
Find the coefficient of correlation of two uncorrelated variables x and y.
7.
Write the normal equations for the curve x = b + cy.
8.
Define sampling error and confidence interval.
9.
Define Type-I error.
10. Define degrees of freedom.
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SECTION-B
11. a) Calculate standard deviation from the table giving age distribution of 542 members :
Age group
20-30
30-40
40-50
50-60
60-70
70-80
80-90
No. of members
3
61
132
153
140
51
2
b) The first four moments of a distribution about the value 4 of the distribution are ?1.5,
17, ?30 and 108. Find the moments about mean.
12. a) Estimate E (X) and E (X)2 from the following probability distribution :
X
?3
6
9
P(X)
1/6
1/2
1/3
b) A can hit a target 3 times in 5 shots, B 2 times in 5 shots and C 3 times in 4 shots. All
of them fire one shot each simultaneously at the target. What is the probability that
(i) 2 shots hit (ii) at least 2 shots hit?
13. a) During war 1 ship out of 9 was sunk on an average in making a certain voyage. What
was the probability that (i) exactly 3 out of a convoy of 6 ships would arrive safely
(ii) a minimum of 7 ships would arrive safely.
b) A car hire firm has two cars which it fires out day by day. The number of demands
for a car on each day is distributed as Poisson variate with mean 1.5. Calculate the
proportion of days on which (i) neither car is used, and (ii) some demand is refused.
14. a) If X is normally distributed and the mean of X is 2 and standard deviation is 4. Find
out the probability of the following :
(i) X 20 (ii) 0 X 12.
b) Calculate the coefficient of correlation for the following height (in inches) of fathers
(X) and their sons (Y) :
X
65
66
67
67
68
69
70
72
Y
67
68
65
68
72
72
69
71
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SECTION-C
15. The diameter of an electric cable, say X, is assumed to be a continuous random variable
with probability density function f (x) = 6x (1 ? x), 0 x 1,
i) Check that above is p.d.f., (ii) Determine a number b such that P {X < b} = P {X > b}.
16. Fit a parabola of second degree to the data :
X
0
1
2
3
4
Y
1
1.8
1.3
2.5
6.3
17. a) If 60 new entrants in a given university are found to have a mean height of 68.60
inches, and 50 seniors a mean height of 69.51 inches, is the evidence, conclusive that
the mean height of the seniors is greater than that of the new entrants? Assume the
standard deviation of height to be 2.48 inches.
b) A dice is thrown 9000 times and a throw of 3 or 4 is observed 3240 times. Show that
the dice cannot be regarded as an unbiased.
18. a) In an experiment on the immunization of goats from anthrax the following results
were obtained. Derive your inference on the efficiency of the vaccine.
Died of anthrax
Survived
Total
Vaccinated
2
10
12
Not vaccinated
6
6
12
(Take 20.05 for 1 degree of freedom = 3.841)
b) The means of two single large samples of 1000 and 2000 members are 67.5 inches
and 68.0 inches respectively. Can be samples be regarded as drawn from the same
population of standard deviation 2.5 inches? (Test at 5% level of significance).
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 13 February 2021